Abstract : This paper studies probability density estimation on the Siegel space. The Siegel space is a generalization of the hyperbolic space. Its Riemannian metric provides an interesting structure to the Toeplitz block Toeplitz matrices that appear in the covariance estimation of radar signals. The main techniques of probability density estimation on Riemannian manifolds are reviewed. For computational reasons, we chose to focus on the kernel density estimation. The main result of the paper is the expression of Pelletier’s kernel density estimator. The computation of the kernels is made possible by the symmetric structure of the Siegel space. The method is applied to density estimation of reflection coefficients from radar observations.
https://hal-mines-paristech.archives-ouvertes.fr/hal-01446923
Contributeur : Jesus Angulo
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Soumis le : vendredi 9 juin 2017 - 14:54:14
Dernière modification le : lundi 10 décembre 2018 - 16:14:08
Document(s) archivé(s) le : dimanche 10 septembre 2017 - 13:37:10
Emmanuel Chevallier, Thibault Forget, Frédéric Barbaresco, Jesus Angulo. Kernel Density Estimation on the Siegel Space with an Application to Radar Processing. Entropy, MDPI, 2016, 18 (11), pp.396. ⟨10.3390/e18110396⟩. ⟨hal-01446923⟩
